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A277149
Lexicographically least sequence of nonnegative integers that avoids 9/5-powers.
4
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0
OFFSET
0,117
COMMENTS
This sequence is 13-regular.
More generally, if a/b is a rational number in the interval 5/3 <= a/b < 2 with gcd(b, 2) = 1 and gcd(a, b) = 1, then the lexicographically least sequence of nonnegative integers that avoids a/b-powers is (2 a - b)-regular.
LINKS
Lara Pudwell and Eric Rowland, Avoiding fractional powers over the natural numbers, arXiv:1510.02807 [math.CO] (2015).
FORMULA
a(13 n + 12) = a(n) + 1.
MATHEMATICA
(* This gives the first 2197 terms. *)
SubstitutionSystem[{n_ :> {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, n + 1}}, {0}, {{3}}]
CROSSREFS
Cf. A277143, A277156, A277157 (sequences in the same family).
Sequence in context: A258825 A361162 A118626 * A062892 A118553 A102448
KEYWORD
nonn
AUTHOR
Eric Rowland, Oct 01 2016
STATUS
approved